KANSAS CITY, Mo. (AP) — Patrick Mahomes picked apart the Colts in his postseason debut, the Chiefs defense answered their chorus of critics with a stout performance, and Kansas City rolled to a 31-13 victory over Indianapolis in the divisional round Saturday to end 25 years of playoff frustration.

Mahomes threw for 278 yards while running for a touchdown, and Damien Williams ran through snow and muck for 129 yards and another score, as the Chiefs beat Indianapolis for the first time in five playoff meetings to earn their first AFC title game appearance since January 1994.

"There was a lot of excitement here, the fans were awesome, the defense played amazing and the offense, we did enough to get the win in the end," Mahomes said.

The AFC West champions will play the winner of Sunday's game between the division-rival Los Angeles Chargers and the New England Patriots next weekend for a spot in the Super Bowl in Atlanta.

Andrew Luck was held to 203 yards passing for the Colts, while Marlon Mack was a non-factor on the ground. He had 46 yards rushing before leaving late in the fourth quarter with a hip injury.

With persistent snow turning Arrowhead Stadium into a winter wonderland, the Chiefs waltzed all over a Colts defense that nearly shut out the Texans a week ago. Mahomes and Co. scored on their first three possessions , then again just before halftime, to take a 24-7 lead into the break.

If there was any question whether this would be Kansas City's day, it was answered when Colts kicker Adam Vinatieri missed a 23-yard field-goal try off the upright just before halftime. It was the first time in 22 postseason attempts that he'd missed from that close.

Not that the Chiefs thought they had it wrapped up.

They've had bigger playoff meltdowns against the Colts.

There was the 10-7 loss in which Lin Elliott missed three field goals when the Chiefs were the No. 1 seed, and the loss at Arrowhead Stadium in 2003 in which nobody punted.

Five years ago, they blew a 38-10 second-half lead against Luck and the Colts to spoil Andy Reid's first season.

Not this time.

Not with this Kansas City quarterback.

After shattering nearly every franchise passing record, Mahomes picked up right where he left off in his regular-season finale. He led the Chiefs on touchdown drives of 90 and 70 yards to open the game, quickly identified a favorite target in Travis Kelce, and shook off a banged-up knee to scramble for a touchdown late in the first half to give his team a big cushion.

Of course, the Chiefs didn't need it the way their defense was playing.

The Colts went three-and-out on their first four possessions, were outgained 185-12 in the first quarter, and Luck didn't complete a pass until he found T.Y Hilton early in the second.

Even when the Colts caught a break and Sammy Watkins fumbled the ball to them late in the third quarter, they were quick to give it back. Dee Ford stripped Luck and fellow linebacker Justin Houston plopped on the ball, ruining another red-zone opportunity.

The Colts finally scored an offensive touchdown with 5:31 left in the game. But in the perfect summation of their lousy afternoon, their erstwhile star kicker missed the extra point.

By that point, the party in the stands already had begun.

The Chiefs had lost six straight home playoff games, including heartbreakers to Pittsburgh and Tennessee the past two years. But a proud franchise that won its only Super Bowl title with Len Dawson in 1970, and last played for a spot behind Joe Montana, is once more one step away.

SNOWBALL FIGHT

Chiefs coach Andy Reid was summoned to the corner of the stadium during the two-minute warning in the first half to implore fans to stop throwing snowballs on the field. Earlier in the half, one almost hit Colts punter Rigoberto Sanchez while he was kicking.

INJURIES

Colts: Center Ryan Kelly (knee) left late in the fourth quarter. ... FS Malik Hooker (foot) and DE Tyquan Lewis (knee) were inactive, while SS Mike Mitchell (calf) was placed on injured reserve earlier this week. That left the Colts defense without some key pieces.

Chiefs: Safety Eric Berry (heel) and running back Spencer Ware (hamstring) were inactive, though Berry — the team's emotional leader — broke down the pregame huddle in the north end zone.